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arXiv · 2606.27272

MLC for parabolically bounded primitive renormalization

Jeremy Kahn·Alex Kapiamba·Mikhail Lyubich
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Abstract

We prove $\textit{a priori}$ bounds and MLC (local connectivity of the Mandelbrot set $\mathcal{M}$) for a class of infinitely renormalizable parameters whose renormalization type is primitive but can approach the cusp of $\mathcal{M}$. To this end we develop and refine a variety of tools that allow us to control degeneration of renormalizations. They include the Thin-Thick Decomposition, the Value Calculus, the Wanderers Theorem, and the Wave Lemma.

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Jeremy Kahn, Alex Kapiamba, Mikhail Lyubich. 2026-06-25. MLC for parabolically bounded primitive renormalization. https://arxiv.org/abs/2606.27272

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